Wind turbine rotor blade with in-plane sweep and devices using same, and method for making same

ABSTRACT

A wind turbine includes a rotor having a hub and at least one blade having a torsionally rigid root, an inboard section, and an outboard section. The inboard section has a forward sweep relative to an elastic axis of the blade and the outboard section has an aft sweep.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH & DEVELOPMENT

The U.S. Government has certain rights in this invention as provided forby the terms of Contract No. ZAM-7-13320-26 awarded by the Department ofEnergy, National Renewable Energy Laboratory Division, under PrimeContract No. DE-AC36-83CH10093 with the U.S. Department of Energy.

BACKGROUND OF THE INVENTION

This invention relates to blades that are particularly useful as windturbine rotor blades and to rotors and wind turbines utilizing suchblades.

At least one known rotor blade configuration includes an aft-swept rotorblade design. When a wind gust strikes a blade with aft sweep, anincrease in out-of-plane (flapwise) loading produces a pitching momentabout sections further inboard. This pitching moment acts to induceouter portions of the blade to twist the leading edge of the bladesections into the wind so as to reduce an aerodynamic angle of attack ofthose sections, thereby ameliorating peak transient loads that the bladewould otherwise experience. However, if the root of the blade remainsunswept or is swept aft, the pitching moment induced over the entireblade is reacted at the root of the blade through pitch drive hardware.For even modest sweep, this moment can overwhelm baseline aerodynamicpitching moments for which the pitch hardware is designed. In otherwords, although in-plane aft sweep of wind turbine rotor blades can beused to ameliorate transient loads, aft sweep also induce pitchingmoments at the blade root that can overwhelm the baseline aerodynamicpitching moments for which the pitch hardware is designed.

For example, many known straight swept blades with zero root sweepexhibit very high changes in root torsion due to coupling. The same istrue of some curved blades designed without a constraint on roottorsion. At least one known baseline configuration exhibits a maximumnose-down pitching moment about the blade root of approximately 30-40kNm. In some swept blades, the nose-down moment increases to hundreds ofkNm. Pitch drives on at least one known wind turbine model, the GE 1.5turbine available from General Electric Co., Fairfield, Conn. aredesigned, with safety factors included, for 100 kNm applied load.Therefore, increases in nose-down moment of more than 20-30 kNm shouldbe avoided.

BRIEF DESCRIPTION OF THE INVENTION

Some aspects of the present invention therefore provide a blade having atorsionally rigid root, a forward sweep relative to an elastic axis inan inboard section of the blade and an aft sweep in an outboard sectionof the blade.

In other aspects, the present invention provides a rotor for a windturbine. The rotor has a hub and at least one blade having a torsionallyrigid root, an inboard section, and an outboard section. The inboardsection has a forward sweep relative to an elastic axis of the blade andthe outboard section has an aft sweep.

In still other aspects, the present invention provides a wind turbinethat includes a rotor having a hub and at least one blade having atorsionally rigid root, an inboard section, and an outboard section. Theinboard section has a forward sweep relative to an elastic axis of theblade and the outboard section has an aft sweep.

In yet other aspects, the present invention provides a method for makinga blade for a wind turbine. The method includes determining a bladeshape by selecting sweep angles for elements of said blade so as to (a)increase or maximize an amount of twist induced and the distribution ofthe twist in such a manner as to create a reduction loads, (b) reduce orminimize an increase in blade material necessary to maintain tipdeflection, (c) reduce or minimize negative effects on aerodynamics, and(d) maintain structural integrity, and fabricating a blade in accordancewith the determined blade shape.

It will be appreciated that, when rotor blades are swept forward by theproper amount, configurations of the present invention reduce oreliminate a pitching moment at blade roots resulting from sweep. Also, aforward sweep of inboard sections of the rotor blades will not produce aharmful twist of measurable magnitude in those sections because theblade root is torsionally extremely rigid. Because the sweep of outboardsections of the blade remains unchanged relative to sections furtherinboard in configurations of the present invention, the twist induced bythe outboard sweep also remains unchanged.

It will also observed that configurations of the invention presentinvention produce beneficial coupling between a flapwise (that is,out-of-plane) deflection of a rotor blade and twisting (that is,pitching) of the rotor blade with little or no increase in root pitchtorque. Coupled twisting of the rotor blade also produces a generalreduction in transient loads experienced by the wind turbine. Forwardsweep inboard also enables greater sweep-induced coupling magnitude fora blade geometry that will fit within a given geometric envelope.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a drawing of an exemplary configuration of a wind turbine ofthe present invention.

FIG. 2 is graphical representation of a moderately swept bladeconfiguration of the present invention suitable for use in the windturbine configuration represented in FIG. 1.

FIG. 3 is a graphical representation of a highly swept bladeconfiguration of the present invention suitable for use in the windturbine configuration represented in FIG. 1.

FIG. 4 is a graphical representation of a blade based upon a prior artwind turbine blade.

In FIGS. 2, 3, and 4, the plane of the paper is the plane of the rotor.The line at the left end of the graph can be interpreted as a blade hubor blade root bearing. The X-axis corresponds to the pitch axis P,whereas a line through the blade and denoted by E represents the elasticor structural axis of the blade. The trailing edge of each blade is atthe top of the figure, and the leading edge is at the bottom. The bladesare thus facing downward.

DETAILED DESCRIPTION OF THE INVENTION

As used herein, the term “sweep” refers to an angle of an elastic axisrelative to a pitch axis of a blade, where the “elastic axis” refers toa locus of points defining a torsional center at each spanwise sectionof the blade.

In some configurations and referring to FIG. 1, a wind turbine 100 insome configurations comprises a nacelle 102 housing a generator (notshown in FIG. 1). Nacelle 102 is mounted atop a tall tower 104, only aportion of which is shown in FIG. 1. Wind turbine 100 also comprises arotor 106 that includes one or more rotor blades 108 attached to arotating hub 110. Although wind turbine 100 illustrated in FIG. 1includes three rotor blades 108, there are no specific limits on thenumber of rotor blades 108 required by the present invention.

Various components of wind turbine 100 in the illustrated configurationare housed in nacelle 102 atop tower 104 of wind turbine 100. The heightof tower 104 is selected based upon factors and conditions known in theart. In some configurations, one or more microcontrollers comprise acontrol system are used for overall system monitoring and controlincluding pitch and speed regulation, high-speed shaft and yaw brakeapplication, yaw and pump motor application and fault monitoring.Alternative distributed or centralized control architectures are used insome configurations. The pitches of blades 108 can be controlledindividually in some configurations. Hub 110 and blades 108 togethercomprise wind turbine rotor 106. Rotation of rotor 106 causes agenerator (not shown in the figures) to produce electrical power.

In some configurations of the present invention, rotor blades 108 of awind turbine 100 are swept forward relative to an elastic axis E (in aplane of rotation of the rotor) in an inboard region 112. When sweptforward by a proper amount, a pitching moment of blade 108 at theirroots 114 due to sweep is reduced or eliminated. Forward sweep ofinboard sections 112 of rotor blades 108 do not produce adverse twist ofmeasurable magnitude of sections 112 because blade roots 114 are istorsionally extremely rigid. Because the sweep of outboard sections 116of blades 108 remains unchanged relative to sections further inboard,twist induced by the outboard sweep also remains unchanged.

In some configurations and referring to FIG. 2, blades 108 include amoderate sweep inboard on the order of 1 to 2 degrees relative to bladepitch axis P, while outboard sections 116 are swept aft up to 10 degreesrelative to pitch axis P. Configurations of the present invention areapplicable to blades 108 of any length. For example, and not by way oflimitation, in some configurations, blades 108 are 0.5 meters long,while in other configurations, blades 108 are 50 meters long. Othernon-limiting examples of blade 108 lengths include 10 meters or less, 20meters, 37 meters, and 50 meters. Although the optimum forward inboardsweep can vary for different blade lengths, a forward inboard sweep ofas little as 0.25 degrees is used in some configurations of the presentinvention. This amount of inboard sweep is greater than themanufacturing tolerance for a blade with zero sweep mounted on a hub andprovides some benefit of root torsion control as an unexpected benefit.In some configurations of the present invention, a greater benefit isachieved with a blade 108 having at least 0.5 degrees of inboard forwardsweep. In some configurations, at least 1.0 degrees of inboard forwardsweep is used, or even more, e.g., 2.0 to 3.0 degrees. In someconfigurations and referring to FIG. 3, more significant twist-flapcoupling is achieved with outboard sections swept as much as 20 degreesrelative to pitch axis P, with an inboard sweep of up to 10 to 15degrees forward to relieve the incremental pitch torque. In manyconfigurations, the amount of aft sweep outboard is less than the amountof forward sweep at the root of the blade.

FIG. 4 is a drawing of one example of a blade 308 that is based upon aprior art GE 37 a blade. Both blades 308 of FIG. 4 and blade 108 ofeither FIG. 2 or FIG. 3 require the same geometric envelope fortransportation purposes. Table I below shows the difference in tip twistthat is induced by blade sweep when blade 108 and blade 308 are undermaximum flapwise load as estimated from computational modeling, and thecorresponding root pitch torque due to the sweep. It is apparent thatblade 108 with both forward and aft sweep produces greater coupling withno increase in pitch torque. TABLE I BLADE: NO FORWARD FORWARD SWEEPSWEEP (308) INBOARD (108) Root Sweep (degrees 0 −2.9 positive representssweep in the aft direction) Blade envelope width (m) 3.6 3.6 Tip TwistUnder Load 4.69 5.52 (degrees) Root Pitch Torque due to 68.2 0 Sweep(kNm)

An aerodynamic center of outboard sections 116 lie aft (in a tangentialsense) of elastic axis E of sections further inboard. As a result, theforce normal to the plane of rotor 106 at a given section 116 willinduce a significant nose down pitching moment about elastic axis Einboard of that station. This pitching moment will in turn cause blade108 to twist nose down at all stations inboard. More importantly,however, when a wind gust strikes blade 108, the gust will induce anincrease in an angle of attack experienced by an outboard section 116and hence increase the lift produced by sections 116. That increase inlift will in turn induce a nose-down twisting of blade 108, whichoffsets some of the increased angle of attack, thereby relieving some ofthe gust-induced load.

By way of further explanation, consider an elemental model of a sweptblade. In this type of model, a blade 108 is modeled as a plurality ofspanwise elements of blade 108. Assume that the in-plane location of theclassic axis relative to the pitch axis is given by the functiony_(ea)(z), where Y_(ea)(0)=0 is presumed. (Note that all references toblades and blade sections utilize reference numerals already introducedin FIGS. 1 and 2, even though the shapes of the blades being discussedwith reference to the model as well as the relative lengths of thesections may differ from that shown in FIGS. 1 and 2.)

First assume that the aerodynamic loading is uniform over each element,such that the net force acts through the mid-point of the element.Calculating forces, V, and moments, M, for each element relative to theaxis of that element allows a simple analysis. From the geometry, foreach element, i, the following relationships apply: $\begin{matrix}{V_{{inboard},i} = {V_{{outboard},i} + V_{{mid},i}}} & (1) \\{M_{y,{inboard},i} = {{\left( {V_{{outboard},i} + {\frac{1}{2}V_{{mid},i}}} \right){\Delta\ell}_{i}} + M_{{youtboard},i}}} & (2) \\{M_{y,{outboard},i} = {{\left( M_{y,{outboard},{i + 1}} \right){\cos\left( {\theta_{i + 1} - \theta_{i}} \right)}} - {\left( M_{z,{inboard},{i + 1}} \right){\sin\left( {\theta_{i + 1} - \theta_{i}} \right)}}}} & (3) \\{M_{z,{outboarrd},i} = {{\left( M_{y,{inboard},i} \right){\sin\left( {\theta_{i + 1} - \theta_{i}} \right)}} + {\left( M_{z,{inboard},{i + 1}} \right){\cos\left( {\theta_{i + 1} - \theta_{i}} \right)}}}} & (4) \\\begin{matrix}{M_{z,{inboard},i} = M_{z,{outboard},i}} \\{= M_{z,i}}\end{matrix} & (5)\end{matrix}$where indices i refer to discrete spanwise elements on a blade, such asare used to analyze the blade in turbine dynamics simulation software;the subscript notations outboard or inboard refer, respectively to theloads at the outboard or inboard end of each such element; M_(y) andM_(z) refer, respectively, to the flapwise (out-of-plane) and torsionalmoments; θ refers to the angle of the element elastic axis relative tothe blade pitch axis, as measured in the plane of rotation; and Δl_(i)is the length of the element i, given by: $\begin{matrix}{\quad{{\Delta\quad\ell} = {\sqrt{\left( {y_{i_{outboard}} - y_{i_{inboard}}} \right)^{2} + \left( {z_{i_{outboard}} - z_{i_{inboard}}} \right)^{2}} = {\frac{\Delta\quad z_{i}}{\cos\quad\theta_{i}}.}}}} & (6)\end{matrix}$

The increase in twist across any element is then given by:$\begin{matrix}{{\Delta\quad\psi_{i}} = {\frac{M_{z,i}}{({GJ})_{i}}\Delta\quad\ell_{i}}} & (7)\end{matrix}$where GJ is the torsional stiffness of the blade and the cumulativetwist at the outboard end of any element i is given by: $\begin{matrix}{\psi_{{outboard},i} = {\sum\limits_{1}^{i}\quad{\Delta\quad{\psi_{i}.}}}} & (8)\end{matrix}$

The sign convention here is such that it is assumed that the positive Vforces of interest are the flapwise forces directed downward (i.e., outof plane), positive sweep angles, θ, correspond to sweeping the bladesections towards the trailing edge (i.e., aft in a tangential sense),and positive pitching moments, M_(z), are such as to induce positive(i.e., nose up) twist, Δψ. Various configurations of the presentinvention provide nose-down twist.

Equations (4) and (5) show that the loading outboard of an element iinduces a pitching moment on that element whenever there is a change insweep angle at the outboard end of that element. This fact demonstratesthat the pitching moment, M_(z), can only increase whenever there is achange in the sweep. If θ_(i)=θ_(i+1), then the sine term in equation(4) is zero, M_(z,outboard,i)=M_(z,inboard,i+1),M_(z,inboard,i)=M_(z,inboard,i+1), and there is no increase in M_(z), sothat changes in sweep are necessary to produce increases in pitchingmoment.

More particularly, the sweep of outboard sections 116 must be measuredrelative to elastic axis E inboard and not relative to some arbitraryaxis such as pitch axis P. Thus, various configurations of the presentinvention do not simply sweep blade 108 straight from root 114. Astraight blade 108 with only a knee at root 114 will experience nopitching moment along its entire length because no sections are actuallyswept with respect to elastic axis E itself, except for the kink at thevery root 114. All of the pitching moment will be absorbed solely atroot 114. However, at root 114, the torsional stiffness is so high thatlittle twisting will occur.

Equations (4) and (5) also show that the greater the change in anglefrom element to element (and hence, the greater the tangential offset ofeach subsequent section), the greater will be the twist-inducing moment.However, large amounts of sweep can also provide negative consequences.Namely, if the total length of a blade 108 measured along elastic axis Eis maintained, then the radius of blade 108 must be reduced.Alternatively, if the radius of blade 108 is maintained, then as blade108 is swept, the length of blade 108 will grow. Either approachadversely affects energy capture, blade weight, and/or stiffness.

By measuring the total sweep in terms of tangential (i.e., y)displacement of blade tip 120 relative to root 114 of elastic axis E,equation (6) yields the following relationship for the displacement oftip 120: $\begin{matrix}{y_{tip} = {{\sum\limits_{i = 1}^{N}\quad{\Delta\quad\ell_{i}\sin\quad\theta_{i}}} = {\sum\limits_{i = 1}^{N}\quad{\Delta\quad z_{i}\tan\quad{\theta_{i}.}}}}} & (9)\end{matrix}$In some configurations of the present invention, the radius of blade 108is maintained at a baseline value R. It then follows that:$\begin{matrix}{R = {\sqrt{y_{tip}^{2} + z_{tip}^{2}} = {\sqrt{\left\lbrack {\sum\limits_{i = 1}^{N}\quad{\Delta\quad z_{i}\tan\quad\theta_{i}}} \right\rbrack^{2} + \left\lbrack {\sum\limits_{i = 1}^{N}\quad{\Delta\quad z_{i}}} \right\rbrack^{2}}.}}} & (10)\end{matrix}$

Knowing that the shortest distance between two points is a straightline, it follows from equations (6) and (10) that the shortest blade 108with the greatest sweep in terms of tangential displacement of tip 120is a straight blade 108 that sweeps from its root 114. However, thisblade will probably induce little if any twist due to the torsionalrigidity of root 108. It also follows that this blade will exhibit theminimum peak sweep. More specifically, if one tries to achieve the sametip displacement with another shape, some section of blade 108 willexhibit higher sweep. For example, a curved blade with elastic axis Eparallel to pitch axis P at root 114 will necessarily have to curve moreoutboard in order to achieve the same displacement at tip 120. Thisblade will be longer. Furthermore, higher sweep angles will also createa negative aerodynamic impact that can be difficult to quantify.

Therefore, in some configurations of the present invention, a blade ismade by first determining a blade shape 108 by selecting sweep angles ofeach element so as to:

-   -   (a) increase or maximize the amount of twist induced and the        distribution of the twist in such a manner as to create a        reduction in loads,    -   (b) reduce or minimize the increase in blade material necessary        to maintain tip deflection,    -   (c) reduce or minimize negative effects on aerodynamics, and    -   (d) maintain structural integrity.

The blade is then fabricated in accordance with the determined bladeshape.

The four objectives (a)-(d) above are not necessarily consistent withone another, so rather than attempting to achieve each objective, aFigure of Merit is defined that allows one to weight the contributionsof all of the effects into one measure. In some configurations of thepresent invention, the Figure of Merit is related to the cost of energy.(The Figure of Merit can be defined so that a higher value represents abetter solution, although it could also be defined so that a lower valuerepresents a better solution. Without loss of generality, it will beassumed herein that a higher Figure of Merit represents a bettersolution, although one of ordinary skill in the art would be able toperform the necessary mathematical manipulations to achieve equivalentresults using Figures of Merit for which the reverse is true.) Variousconfigurations of the present invention provide a high Figure of Merit,i.e., a low cost of energy. Ideally, the maximum possible Figure ofMerit is sought, but the invention also includes within its scopedesirable, but less than perfect configurations, as perfection is notrequired to achieved at least some of the advantages of the presentinvention.

In any practical configuration, it can be expected that a constraintwill be placed on maximum tip tangential displacement, and that thisconstraint may relate to manufacturing or transportation limitations.Equation (4) shows that if one simultaneously imposes a fairly severeconstraint on the location of tip 120 and also a constraint on themaximum sweep angle due to aerodynamics, then the “optimum” blade 108 isone that has two straight segments, namely, an inboard segment 112having no sweep and an outboard segment 116 that has the maximumallowable sweep. Outboard of a knee between segments 112 and 116, thereis no pitching moment, and inboard of the knee there is a constantpitching moment, which places the pivot point as far outboard aspossible, so that the maximum spanwise extent of blade 108 is subjectedto the pitching moment. In this configuration, the maximum possibletwist is induced.

It is further possible to add an additional “aesthetic” constraint thateliminates sharp knees in the blade sweep. Such constraints can take onmany forms, such as a maximum change in angle between any two elementsof blade 108. Aesthetics could further dictate that a blade 108 havingcontinuous curvature is more appealing than a blade 108 having straightsections, even if the straight sections are connected by a curved regionrather than a knee. Such a constraint could be imposed in the form of aminimum angle between any two elements.

Once all of these constraints are imposed, some configurationsiteratively select values for sweep angles of spanwise elements of ablade 108 so as to maximize (or at least increase) the Figure of Meritwhile satisfying all the constraints.

The location of elastic axis E (as opposed to pitch axis P) relative tooutboard section or sections 116 is significant. The location of pitchaxis P of blade 108, which is controlled entirely by how blade 108 ismounted to hub 110, has nothing to do with how much blade 108 willtwist. The location of outboard section or sections 116 relative topitch axis P, however, does have an influence on the moments inducedabout blade root 114 that a pitch system must withstand, and that is oneof the costs of inducing blade twist in the manner described herein.However, this cost does not influence the physics of the twist-bendcoupling.

More particularly, various methods for mounting blade 108 to root hub110 are possible, each having its own costs and advantages. For example,equation (4) indicates that if blade 108 is actually swept forward(i.e., in-plane) at root 114 in the opposite direction from all theother sweep of blade 108, this forward sweep can be used to neutralizeall of the pitching moment built up by blade sweep further outboard. Inother words, if blade 108 is swept aft over the spanwise extent where itis torsionally flexible enough to induce twist, the all of thatsweep-induced moment can be taken back out with a small region ofspanwise sweep near root 114 where it is torsionally rigid. In such aconfiguration, there is no effect on the twist induced by the sweep, butthe external pitching moment to which a pitch bearing and drive mustreact is reduced or eliminated.

To effect this reduction in sweep-induced moment, some configurations ofthe present invention provide a forward sweep of blades 108 only attheir roots 114. Although some other configurations can introduce aforward sweep into hub 110, such other configurations would still haveto have pitching moments taken out by the bearing and drives.

Referring again to equations (4) and (5), if the notation i=0 is used torefer to the values at the very root 114 of blade 108 (i.e., hub mount),and further noting that θ₀=0 by definition, it follows that:M _(z,0)=−(M _(y,inboard,1))sin(θ₁)+(M _(z,inboard,1))cos(θ₁).  (11)At first glance, it may not be evident that M_(z,0) does not equalM_(z,inboard,1). However, the pitching moment is always measured aboutelastic axis E of the element, and so if the angle of the elementchanges, the axis about which the moment is measured changes. At root114, the structure of blade 108 actually carries the torsionM_(z,inboard,1). However, blade 108 is stiff with respect to torsion atroot 114, so the fact that the structure of blade 108 carries torsionM_(z,inboard,1) is largely irrelevant, and the value of M_(z,0), whichis directly related to the loads carried by the pitch actuator, is morerelevant. Therefore, simply by sweeping root 114 of blade 108, thefundamental relationship between M_(z,0) and M_(z,inboard,1) is changed.

From a practical perspective, any particular configuration must effectthe forward sweep over a finite span. However, so long as this sweep iseffected over a portion of blade 108 that is torsionally highly rigid,the forward sweep will not induce adverse twisting.

The value of M_(y,inboard,1), that is, the flapwise loading at root 114,is largely a function of the flapwise loading distribution over blade108. The value of M_(z,inboard,1) is dependent upon the magnitude andshape of the sweep over the full span of blade 108 and the distributionof flapwise loading. Equations (1) through (5) can be integratedstarting at the tip element and moving inboard to calculate the loads onevery spanwise element. Given some distribution of in-plane sweep andflapwise loading distribution, the value of M_(z,inboard,1) will be agiven. Once that value is known, then value of the root torsion,M_(z,0), can be found using equation (11). Conversely, if a certainvalue of the root torsion is sought, then equation (11) can be used tofind the appropriate value of the sweep of the first element θ₁.

Specifically, if in some configuration, a zero net effect on roottorsion is desired, then equation (11) is used to solve for:$\begin{matrix}{{\theta_{1} = {\tan^{- 1}\left\{ \frac{M_{z,{inboard},1}}{M_{y,{inboard},1}} \right\}}},} & (12)\end{matrix}$

-   -   which defines the optimum root forward sweep for zero net change        in root torsion due to sweep.

When a wind gust strikes a blade 108 with aft sweep, the increase inout-of-plane (flapwise) loading also produces a pitching moment aboutsections further inboard that will act to induce the outer portions ofthe blade to twist the leading edge of the blade sections into the wind.The aerodynamic angle of attack of those sections is reduced, therebyameliorating the peak transient loads which blade 108 would otherwiseexperience. Such twist-flap coupling through sweep results insubstantial reductions in blade 108 flapwise transient loads, reducingboth the ultimate flapwise loads and blade flapwise fatigue. Aft sweepcan also generally produce reductions in other components of the loadingof wind turbine 100, including tower top thrust force and tower top tiltand yawing moments. These load reductions translate into reductions incost of energy from wind power by either removing expensive materialfrom components subjected to the lighter loading of swept blade 108 orby increasing the diameter of blades 108 of rotor 106 to increase theenergy production of wind turbine 100.

Table II, concerning the use of forward sweep at the root to zero roottorsion, compares a blade with no forward sweep at its root to onehaving a forward swept root in which the entire blade is tilted forwardby a few degrees. Table II shows that, by sweeping the blade forward atthe root, root torsion can be eliminated because the blade is sotorsionally stiff at the root that introducing forward sweep there haslittle or no impact on the twist response of the blade. From thereoutboard, the blade looks exactly the same, and so the twist response tosweep is exactly the same. TABLE II No Forward Forward Parameter Sweepat Root Swept Root Location of elastic axis at 3.000 1.572 tip, yea, tip(m) Location of tip trailing 3.420 1.992 edge, yTE, tip (m) Depth ofsweep (m) 1.50 1.50 Change in tip twist at −1.79 −1.79 baseline maxdeflection (degrees) Effective coupling 0.052 0.052 coefficient Increasein root torsion 88.82 1.05 (kNm) Blade envelope height (m) 3.281 2.444Blade envelope width (m) 2.919 2.346 Permissible change in  0.9%  0.9%rotor diameter Net effect on cost of −0.55% −0.60% energy

Another benefit of configurations of the present invention is that ifthe radius of rotor 106 is maintained, as blades 108 are rotatedforward, the blade length, measured along elastic axis E, is reducedvery slightly. This reduction accounts for the 0.05% improvement in costof energy shown in Table II for the blade with forward root sweep.

Yet another benefit of sweeping blade 108 forward at root 114 is thatthe blade envelope is reduced for a given depth of sweep. For a givenconstraint on the envelope, allowing root 114 to sweep forward providesfor a much greater depth of sweep.

In deference to aerodynamic considerations, some configurations of thepresent invention impose a constraint on the maximum sweep angle of anyelement. In such configurations, blades 108 have a maximum sweep forwardat root 114 and the maximum sweep aft in outboard section 116 with asharp knee. For example, for 15 degree maximum angle, someconfigurations of blade 108 have a 15 degree forward sweep at root 114and a knee at 60% span with 15 degree aft sweep at tip 120.

Configurations of the present invention can be applied to an existingwind turbine 100 by replacing conventional blades with swept blade 108configurations of the present invention blade without requiringexpensive upgrades of pitch drive hardware, allowing full realization ofthe potential for reducing the cost of energy. Furthermore, forwardsweep inboard also enables a greater magnitude of sweep-inducedtwist-flap coupling for a blade geometry that will fit within a givengeometric envelope.

While the invention has been described in terms of various specificembodiments, those skilled in the art will recognize that the inventioncan be practiced with modification within the spirit and scope of theclaims.

1. A blade having a torsionally rigid root, a forward sweep relative toan elastic axis in an inboard section of said blade and an aft sweep inan outboard section of said blade.
 2. A blade in accordance with claim 1wherein said forward sweep is at least 0.25 degrees.
 3. A blade inaccordance with claim 1 wherein said forward sweep is at least 0.5degrees.
 4. A blade in accordance with claim 1 wherein said forwardsweep is at least 1 degree.
 5. A rotor for a wind turbine, said rotorhaving a hub and at least one blade having a torsionally rigid root, aninboard section, and an outboard section, said inboard section having aforward sweep relative to an elastic axis of said blade and saidoutboard section having an aft sweep.
 6. A rotor in accordance withclaim 5 wherein said blade has a forward sweep of at least 0.25 degrees.7. A rotor in accordance with claim 5 wherein said blade has a forwardsweep of at least 0.5 degrees.
 8. A rotor in accordance with claim 5wherein said blade has a forward sweep of between 1 and 3 degrees,inclusive.
 9. A rotor in accordance with claim 5 wherein said forwardsweep is effective to counter an amount of torsion resulting from saidaft sweep.
 10. A rotor in accordance with claim 9 wherein said forwardsweep is at a root of said blade and an amount of said forward sweep iseffective to neutralize a pitching moment built up by blade sweepfurther outboard.
 11. A rotor in accordance with claim 5 wherein saidblade has a root, a tip, and a knee at 60% span, and said blade has a 15degree forward sweep at its root and a 15 degree aft sweep at its tip.12. A wind turbine comprising a rotor having a hub and at least oneblade having a torsionally rigid root, an inboard section, and anoutboard section, said inboard section having a forward sweep relativeto an elastic axis of said blade and said outboard section having an aftsweep.
 13. A rotor in accordance with claim 12 wherein said blade has aforward sweep of at least 0.25 degrees.
 14. A rotor in accordance withclaim 12 wherein said blade has a forward sweep of at least 0.5 degrees.15. A rotor in accordance with claim 12 wherein said blade has a forwardsweep of between 1 and 3 degrees.
 16. A rotor in accordance with claim12 wherein said forward sweep is effective to counter an amount oftorsion resulting from said aft sweep.
 17. A rotor in accordance withclaim 16 wherein said forward sweep is at a root of said blade and anamount of said forward sweep is effective to neutralize a pitchingmoment built up by blade sweep further outboard.
 18. A rotor inaccordance with claim 12 wherein said blade has a root, a tip, and aknee at 60% span, and said blade has a 15 degree forward sweep at itsroot and a 15 degree aft sweep at its tip.
 19. A method for making ablade for a wind turbine, said method comprising: determining a bladeshape by selecting sweep angles for elements of said blade so as to (a)increase or maximize an amount of twist induced and the distribution ofsaid twist in such a manner as to create a reduction loads, (b) reduceor minimize an increase in blade material necessary to maintain tipdeflection, (c) reduce or minimize negative effects on aerodynamics, and(d) maintain structural integrity; and fabricating a blade in accordancewith the determined blade shape.
 20. A method in accordance with claim19 further comprising selecting a Figure of Merit and weighting factors(a)-(d) in accordance with the selected Figure of Merit.
 21. A method inaccordance with claim 20 wherein the Figure of Merit is related to costof energy.
 22. A method in accordance with claim 20 wherein the bladehas a tip, and further wherein determining a blade shape furthercomprises imposing a constraint on a location of the tip and on amaximum sweep angle.